Related papers: Arithmetic of matrices over rings
This paper addresses various questions about pairs of similarity classes of matrices which contain commuting elements. In the case of matrices over finite fields, we show that the problem of determining such pairs reduces to a question…
This paper is devoted to the theory of $GL_n({\mathbb Z})$-conjugacy classes of regular integer $n\times n$ matrices. Such a matrix is $GL_n({\mathbb Q})$-conjugate to the companion matrix of its characteristic polynomial. But the set of…
This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include…
The main aim of this paper is to characterize ideals I in the power series ring R=K[[x1,...,xs]] that are finitely determined up to contact equivalence by proving that this is the case if and only if I is an isolated complete intersection…
Arithmetical properties of a finite group are properties of the group which are defined by its arithmetical parameters such as the order of the group, the element orders and so on. In this paper, we discuss a number of results on…
There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold…
Let $R$ be a commutative unital ring. A well-known factorization problem is whether any matrix in $\mathrm{SL}_n(R)$ is a product of elementary matrices with entries in $R$. To solve the problem, we use two approaches based on the notion of…
In order to simultaneously generalize matrix rings and group graded crossed products, we introduce category crossed products. For such algebras we describe the center and the commutant of the coefficient ring. We also investigate the…
This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial,…
The aim of this paper is to analize the structure of BL-algebras using commutative rings. From computational considerations, we are very interested in the finite case. We present new ways to generate finite BL-algebras using commutative…
We observe that there is an equivalence between the singularity category of an affine complete intersection and the homotopy category of matrix factorizations over a related scheme. This relies in part on a theorem of Orlov. Using this…
Orders in an algebraic number field form a class of rings which are of special historical interest to the field of factorization theory. One of the primary tools used to study factorization is elasticity - a measure of how badly unique…
In this paper, two kinds of generalizations of ideal matrices, generalized ideal matrices and double ideal matrices. are obtained and studied, The concepts of generalized ideal matrices and double ideal matrices are proposed, and their…
We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and…
In this paper using the connections between some subvarieties of residuated lattices, we investigated some properties of the lattice of ideals in commutative and unitary rings. We give new characterizations for commutative rings $A$ in…
This article focuses on the study of the group of units of incidence rings, which is a class of infinite matrix groups indexed by ordered sets, on a topological perspective. We first show when these groups can inherit the topological…
In this paper we shall consider the Lie algebra of column-finite infinite matrices indexed by positive integers $\mathbb{N}$, describe the lattice of its ideals for arbitrary field $K$ and study its derivations over any commutative, unital…
In the context of applying the Lorentz group theory to polarization optics in the frames of Stokes-Mueller formalism, some properties of the Lorentz group are investigated. We start with the factorized form of arbitrary Lorentz matrix as a…
We present a sufficient condition for irreducibility of forcing algebras and study the (non)-reducedness phenomenon. Furthermore, we prove a criterion for normality for forcing algebras over a polynomial base ring with coefficients in a…
We develop a functorial framework for the ideal theory of commutative semirings using coherent frames and spectral spaces. Two central constructions-the radical ideal functor and the $k$-radical ideal functor-are shown to yield coherent…